This invention relates to high frequency (HF) radio signal propagation through fading channels and, more particularly, to simulation of fading channels in order to characterize HF radio system performance in transmitting and receiving signals through such fading channels. This invention is the result of a contract with the Department of Energy (Contract No. W-7405-ENG-36).
HF radio signals propagate through the ionosphere along a variety of paths of different length ("multipaths") and with different propagation characteristics. Interference arises between the signals on the various paths producing signal fading on time scales from a fraction of a second to a few seconds, whereby the "fading channels" produce a degradation of the signal quality. Methods of modulation, diversity, and coding in the system design are selected in order to minimize this signal degradation.
Testing of HF communication systems can be done by using operational systems either through a real circuit, or through a channel simulator. Real circuit tests can be expensive, and may not provide actual "worst case" situations. Alternately, one must ensure that the channel simulator accurately depicts the effects of a "real" channel.
HF ionospheric channels are nonstationary in both frequency and time, but for narrow bandwidths (tens of kHz) and short times (minutes) most channels can be adequately represented by a stationary model. In addition, except under extreme conditions, the ionosphere supports propagation over a limited number of discrete modes representing different average signal levels and delays. Moreover, each path will show a different fading rate and delay spread.
A radio channel may be modeled as a randomly time-varying linear channel that can be characterized by a channel scattering function. This scattering function is defined as the density of power scattered by the channel as a function of Doppler shift, time delay, and spatial angle-of-arrival. A received HF signal is usually the composite of several signals arriving via different ionospheric propagation modes, and the signal power is spread in the three dimensions of time, frequency, and arrival angle.
Time spreading is the result of the signal propagating via two or more paths having slightly different propagation times. Frequency spreading is the result of movements of the reflecting ionospheric layers and of the time variation of the electron density along the ray paths, both of which cause changes in the phase of the received signal. The rate of change of phase can be interpreted as a Doppler shift of the transmitted frequency.
A line-of-sight propagation channel can be characterized by a linear filter described by a gain G(f,t) and a propagation time delay t.sub.o, where G(f,t) is likely to be a complex valued function. The time varying frequency response of such a channel is: EQU H(f,t)=G(f,t)e.sup.-2.pi.ft o
where f is the frequency and t is the time.
A multipath channel can be described as a linear sum of several such channels, or "modes": EQU H(f,t)=.SIGMA..sub.i[ G.sub.i (f,t)e.sup.-j2.pi.ft i],
where i labels the individual modes.
Signal fading is simply the constructive and destructive interferences generated by the vector addition of the signal propagated through these several channels.
An exemplary channel scattering function is described in Proakis, Digital Communications, McGraw-Hill, New York 1989. See also Bello, "Characterization of Randomly Time-Variant Linear Channels," IEEE Trans. Commun. Systems, pp. 360-393 (December 1963). Both teachings are incorporated herein by reference. A channel correlation function, .phi..sub.c (.DELTA.f,.DELTA.t), describes the correlation in frequency and time of the channel response, H(f,t), and is given by: EQU .phi..sub.c (.DELTA.f,.DELTA.t)=1/2[H.sup.* (f,t)H(F+.DELTA.f, t+.DELTA.t)]
where the square brackets denote the expectation value. The channel correlation function describes the coherence bandwidth and coherence time of the channel. The two-dimensional Fourier transform, S(.tau.,.lambda.), is called the channel scattering function and describes the channel response in delay, .tau., and Doppler frequency, .lambda., where ##EQU1## A form of scattering function is illustrated by FIG. 1, which graphically depicts power density as a function of delay, .tau., and Doppler frequency, .lambda..
Given the Fourier transform relation between the channel correlation function, .phi..sub.c, and the channel scattering function, S, the Wiener-Khintchine theorem may be applied to interpret the channel scattering function, S(.tau.,.lambda.), as the average power spectral density of the random process, H(f,t). Then a realization of H(f,t) may be generated with the known technique of inverse Fourier transforming the random complex process, h(.tau.,.lambda.), whose real and imaginary parts are independent, Gaussian random variables, each with zero mean and variance of S(.tau.,.lambda.)/2.
In the usual characterization of a channel, the gain function (G) is not treated as a function of frequency (f), so that the channel is in reality a "nonselective or multiplicative" fading channel. In this case, all frequencies fade together. In most cases using this characterization, the delay is treated as a fixed delta function in time, with Rayleigh fading imposed upon each modal gain function. Further, in order to generate a statistical model for the short term fading channel, one must assume stationary statistics, i.e., that the mean values of the model parameters are constant. Then the channel model presents a particular realization of a stochastic process.
In one prior art representation, Watterson et al., Experimental Confirmation of an "HF Channel Model," COM-18 IEEE Trans. Commun. Technol., No. 6, pp. 792-803 (1970), showed that the channel can be modeled as a "tapped delay line" with a limited number of taps with adjustable delays. The signal at each tap is modulated in phase and amplitude by a suitable tap-gain function, and the several delayed and modulated signals are summed to form the output signal. The Watterson model uses "independent zero-mean complex-Gaussian functions with Rayleigh amplitude and uniform phase density" to modulate the incoming signal.
It would be desirable to represent the channel transmissions as a function of frequency and to provide nonstationary channel statistics to more accurately model fading channels for HF radio transmission. These problems are addressed by the present invention wherein a channel scattering function is used to represent the channel delay-spread and Doppler-spread functions.
Accordingly, it is an object of the present invention to provide the channel gain function as a function of frequency.
It is another object of the present invention to provide a time varying representation of channel transmissions.
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.